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Deep Learning Web Course
  • Welcome to Math 452

contents

  • Module 0 Get started: course information and preparations:
    • Course information, requirements and reference
    • Course background and introduction
    • Introduction to Python and Pytorch
    • Preliminary Quiz
  • Module 1: Linear machine learning models
    • Machine learning basics, popular data sets
    • Linearly separable sets
    • Logistic regression
    • KL-divergence and cross-entropy
    • Support vector machine and relation with LR
    • Optimization and gradient descent method
    • Homework 1
    • Module 1 Programming Assignment
    • Quiz 1
  • Module 2: Probability and training algorithms
    • Introduction to probability
    • Probabilistic derivation of logistic regression models
    • Convex functions and convergence of gradient descen
    • Stochastic gradient descent method and convergence theory
    • MNIST: training and generalization accuracy
    • Homework 2
    • Week 2 Programming Assignment
    • Quiz 2
  • Module 3: Deep neural networks
    • Nonlinear models
    • Polynomials and Weierstrass theorem
    • Finite element method
    • Deep neural network functions
    • Universal approximation properties
    • Application to data classification
    • DNN for image classification
    • Monte Carlo Methods
    • Building and Training Deep Neural Networks (DNNs) with Pytorch
    • Homework 3
    • Week 3 Programming Assignment
    • Quiz 3
  • Module 4: Convolutional neural networks
    • Convolutional neural networks
    • Convolutional operations on images
    • Some classic CNN
    • Training CNN with GPU on Colab
    • Building and Training Convolutional Neural Networks (CNNs) with Pytorch
    • Homework 4
    • Week 4 Programming Assignment
    • Quiz 4
  • Module 5: Normalization, ResNet and Multigrid
    • Data normalization and weights initialization
    • Batch normalization
    • Building and Training ResNet with Pytorch
    • Multigrid Method for Finite Element
    • Homework 5
    • Week 5 Programming Assignment
    • Quiz 5
  • Module 6: MgNet
    • MgNet: a special CNN based on multigrid method
    • Multigrid and MgNet
    • Multigrid and MgNet
    • MATH 452: Final Project
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Module 3: Deep neural networksΒΆ

  • Nonlinear models
  • Polynomials and Weierstrass theorem
  • Finite element method
  • Deep neural network functions
  • Universal approximation properties
  • Application to data classification
  • DNN for image classification
  • Monte Carlo Methods
  • Building and Training Deep Neural Networks (DNNs) with Pytorch
  • Homework 3
  • Week 3 Programming Assignment
  • Quiz 3

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Nonlinear models

By Jinchao Xu
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